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6 Answers
6

SQL is Structured Query Language is a
database computer language designed
for managing data in relational
database management systems (RDBMS).

PostgreSQL is an object-relational
database management system
(ORDBMS).1 It is released under a
BSD-style license and is thus free
software. As with many other
open-source programs, PostgreSQL is
not controlled by any single company,
but has a global community of
developers and companies to develop
it.

SQLite is an ACID-compliant embedded
relational database management system
contained in a relatively small (~225
KB1) C programming library. The
source code for SQLite is in the
public domain.

MySQL (pronounced /maɪˌɛskjuːˈɛl/1
My S-Q-L, or "My sequel"
/maɪˈsiːkwəl/) is a relational
database management system (RDBMS)2
which has more than 6 million
installations. 3 MySQL stands for
"My Structured Query Language". The
program runs as a server providing
multi-user access to a number of
databases.

SQL, TSQL = the actual languages used by the aforementioned database systems. Although (in theory) SQL is standardised, in practice each vendor has their own "extensions" (variations) on the language - which means that SQL written for MySQL may not work under Sybase, for example.

Different Vendors= Different Ideas and Concepts.
Like every other Programming Problem...every developer solutes it differently and thats great. :-)
Learing about this little differences or sometimes big "Messed up" is good.